To determine the equation of a circle centered at the origin with a given radius, we use the standard form of the circle equation, which is:
[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]
Here, [tex]\((h, k)\)[/tex] is the center of the circle, and [tex]\(r\)[/tex] is the radius.
1. Since the circle is centered at the origin, the center [tex]\((h, k)\)[/tex] is [tex]\((0, 0)\)[/tex].
2. The radius [tex]\(r\)[/tex] is given as 8.
Plugging the center [tex]\((0, 0)\)[/tex] and radius [tex]\(8\)[/tex] into the standard circle equation, we get:
[tex]\[ (x - 0)^2 + (y - 0)^2 = 8^2 \][/tex]
Simplifying this equation, we have:
[tex]\[ x^2 + y^2 = 64 \][/tex]
Therefore, the correct equation of the circle is:
[tex]\[ x^2 + y^2 = 64 \][/tex]
Given the choices:
A. [tex]\(x^2 + y^2 = 8\)[/tex]
B. [tex]\(x^2 + y^2 = 64\)[/tex]
C. [tex]\(x + y = 8\)[/tex]
D. [tex]\(x^8 + y^8 = 64\)[/tex]
The correct option is:
B. [tex]\(x^2 + y^2 = 64\)[/tex]
So, the answer is:
2
